In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable iff it is in the second ambiguous class (boldface Delta^0_2), iff it is eventually annihilated by a certain remainder. We simplify this remainder and give a new proof of the latter equivalence. We then introduce a notion of guessing with an ordinal limit on how often one can change one's mind. We show that for (...) every ordinal alpha, a guessable set is annihilated by alpha applications of the simplified remainder if and only if it is guessable with fewer than alpha mind changes. We use guessability with fewer than alpha mind changes to give a semi-characterization of the Hausdorff difference hierarchy, and indicate how Wadge's notion of guessability can be generalized to higher-order guessability, providing characterizations for boldface Delta^0_alpha for all successor ordinals alpha>1. (shrink)

Abstract. Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi (“Two Flavor's of Curry's Paradox”) call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists”. To (...) this end they recommend a radical solution to both paradoxes, involving a substructural logic, in particular one without structural contraction. -/- Abstract. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the Second Incompleteness Theorem. (shrink)